I'm not so sure, really. But what puzzles me most is how can someone who climbed the Eiger not remember it. Unless you are one of a dozen world top climbers, you would not climb the Eiger alone, you would hire a guide, use a rope, a helmet, a harness, etc.. I don't know the particulars of Sunnyrosa's mother, but "normally" she should remember.

There is no comprehensive list (that I know of) of Eiger climbers. The only lists that I found include only special achievements (first one on a particular route, new time record, etc.). There are so many climbers that it is probably not possible to keep track of all, esp. if you include the non-north-face routes, and incomplete attempts. I guess we'll never know for sure.